The Quadratic Formula

Chapter 4 - Algebra Reference

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Solving for x in a given polynomial equation “ax2 + bx + c =0”, can be solved by factoring the equation. 

Another way is by using Quadratic formula, where it is derived in the process of completing the square. 

Thus, $$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

where x = solutions of the equation

          a, b, c = numerical coefficient 


Example: 

Solve for x using Quadratic Formula given : 6x2 + 11x - 35 = 0
 

Solution:

$$x_{1}=\frac{-(11)+\sqrt{((11^2)-4(6)(-35))}}{2(6)}=\frac{5}{3}$$

 

$$x_{2}=\frac{-(11)-\sqrt{((11^2)-4(6)(-35))}}{2(6)}=-\frac{7}{2}$$